Find and classify the relative extrema of the function, if they exist. You MUST use the first-derivative test. 2x x² +1 .) f(x) =

Q: 14. Determine whether the triangles are similar. If they are, write a similarity statement. Explain…

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Q: Let →r(t)=⟨2t−3,5e^−2t,−2e^2t⟩ Find the line (L) tangent to →r(t)r→(t) t=-3.

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Q: Please, could you explain how do they find the x-limits as functions of y and z? then z-limit as a…

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Q: 1. Integrate using an appropriate method. [2si 2 sin³(r) cos² (r)dr

A: The given integral is: I=∫2sin3xcos2xdx   As we know that; The trigonometric identity; sin2x+cos2x=1…

Q: Determine whether u and v are orthogonal, parallel, or neither. u = (cos(8), sin(0), 1) v = (sin(0),…

A: If u and v are orthogonal then u•v = 0  if u and v are parallel then u • v = | u | •| v |

Q: The maximum rate of change of the function 1 ----> at the point (1,-2) happens in direction of and…

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Q: Solving Differential Equation by Laplace Transform Solve the following initial value problems using…

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Q: Without using a calculator, find the distance traveled by a particle with position (x, y) as t…

A: The distance travelled by the particle is the same as the arc length as varies within the interval…

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

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Q: Use the graph to determine the limit. (If an answer does not exist, enter DNE.) -8 (a) lim f(x) =…

A: To find out the limits.

Q: 3. A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a well…

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Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) ³ + 3x² = C (B) 2y³ + 2x² =…

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Q: Find f'(x) and simplify. f(x)= Which of the following shows the correct application of the quotient…

A: We can solve as follows Do not confuse in round bracket and close bracket. They are same in this…

Q: 3. Find a power series representation for the function f(x) = = 1 x+2 and find its interval of…

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Q: Find the limit. lim (3x-4)

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Q: The gradient vector of the function f(x, y, z)= ln(yz) - x² is: 2 Select one: 0 (-2x,1,1) O None of…

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Q: We are given the initial value y(0) = 2. Substituting this value and solving for L{y} gives the…

A: Solution of given question is written in below steps.

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. [ cos¹…

A: This question is related to indefinite integration, we will solve it using given information.

Q: Find the constant a such that the function is continuous on the entire real line. -√8x², a = ax - 8,…

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Q: Use an iterated integral to find the area of the region bounded by 2x - 5y = 0, x+y=6, y = 0.

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Q: Without using a calculator, for the following, sketch the graph of the polar equation and identify…

A: Follow the procedure given below.

Q: Find an equation for the ellipse whose graph is shown. y 0 (10,5) 15 X

A: Consider the ellipse  Consider the graph

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: I. Perform the indicated multiplication on the differential operator D. (D+2x)(D-3x)

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Q: Find the constant a such that the function is continuous on the entire real line. 2sin x a 11 g(x):…

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Q: 4. Terms of a sequence from sampling a signal. In electrical engineering, a continuous function like…

A: Please see the below picture for detailed solution.

Q: Find the limit (If It exists). (If an answer does not exist, enter DNE.) (x² - 4x +18, -x² + 4x -…

A: Put the condition for existence of a limit and cross check.

Q: ƒ7 In ()dx if sec¹ (3x) dx

A: Integration by parts: ∫f(x)·g(x) dx = f(x)·∫g(x) dx - ∫ddxf(x)·∫g(x) dx dx

Q: Find an equation for the ellipse that satisfies the given conditions. Foci: F(0, ±2), vertices: (0,…

A: Given, Foci: F(0,±2),  vertices: (0,±5)

Q: Ιπ 10. State the exact value of tan- 6

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Q: 2. Integrate using an appropriate method. 1 PVR-36° dr

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Q: If    f(x) = 2 cos(x),    0 ≤ x ≤ 3pi/4,    evaluate the left Riemann sum with  n = 6,  taking the…

A: Given :fx=2cosx   , n=60≤x≤3π4

Q: Find the component of u = 2i + j − 3k that orthogonal to v = 3i – j, then verify your result.

A: This question can be solved using the concept of component of vectors.

Q: xdx + (y − 2x)dy = 0

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: To find the arclength of y = 4x² - 3 from a = 0 to x = 4, which is the correct integral? √ VI + Sada…

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Q: Without using a calculator, for the following, determine whether the graph of the polar equation is…

A: Given that    r = 2 secθ            we know that    x(θ) =  r cosθ      and      y(θ) = r sinθ…

Q: 3. y + 4y'+4y=0

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Q: A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An…

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Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of t…

A: Please see the below picture for detailed solution.

Q: The total sales of S (in thousands of DVD's) of a certain movie are given by the following formula…

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Q: 2. Which definite integral approximation formula is f(x) dx = Left rectangles Right rectangles…

A: The given formula is;  Integration of f(x) , limit from a to b = (b-a) /n [y0+y1+y2+y3+...+yn-1].

Q: For the given demand equation, differentiate implicitly to find dp/dx. ) 40p2 - 300p + 612 = x

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) làm 9 cot x

A: topic- limits

Q: Give an example of a derivable function f (x) with f ′ (- 4) = -3

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Q: Problem 11 (i) Find the area bounded by the polar curves r = 0 + 1, r = 0+3, 0=0, and 0 = 2 (ii)…

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Q: 10 Find lim f(x) given the graph of f(x) shown above. (If the limit does not exist, enter Ø.) 1-2

A: Find the limit from the graph

Q: Solve the problem. 18) A beverage company works out a demand function for its sale of soda and finds…

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Q: 6. Suppose you drop a golf ball onto a hard surface from a height h. The collision with the ground…

A: Disclaimer: Since you have multiple sub parts of question, we will solve first three part for you.if…

Q: 1. Explain why there is no solution to sec() and csc(n). You can use graphs and diagrams if you want…

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Q: Solve the problem. 15) Let f(x) = ex. Round to 6 decimal places as needed. a) Find the linearization…

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